The wipers will freeze and stop working on all settings, but start up again after the car has been stopped for a while. Other things that operate on the same fuse still work.
could be a bad ground wire or the motor is on it's way out
sounds like sticky valves. Get your tranny flushed.
Get it checked out by a shop. Do NOT add trans additives to it! They will ruin the trans!
First lube your wiper linkage - that's what moves the arms. It should be right beneath the windshield. After a while, with the harsh weather and salt, the joints of this mechanism will start to seize - happened to me and I had these exact symptoms. In my case, lubing the linkage worked. If it's too far gone, it can burn out the wiper motor. Then you're looking at changing the linkage AND the motor. The sooner you lube it, the sooner you'll know, and you might even save it in time before the motor burns out.